I would think that it'd be cheaper and easier for you to purchase the font, if possible (presumably you already had things like labels and business cards printed, so they would all have to be re-done as well?). Did you look up how much it costs?
Think of companies like Vogue, Netflix, Uber, flickr... there are a million companies whose logo is basically just a font that has been manipulated. If you own the font, then you are allowed to use it.
It's hard to say without seeing your logo or knowing the font name, but just buy the font from dafont.com and look at the readme file. It will tell you if there are any restrictions and likely also give you the designer's info, whom you can contact if you still have questions.
On the other hand, if the "free" font is actually a ripoff of something like Helvetica or Bodoni, you would be better off purchasing from a more mainstream font source such as fonts.com.